Taurus flowering ash (Fraxinus ornus subsp. cilicica) is an endemic tree species in Turkey. The bark of the species was characterized for summative chemical composition, the monomeric composition of polysaccharides, phenolic content, in vitro and ex vivo antioxidant properties of hydrophilic extracts, the composition of lipophilic extractives and suberin, and thermal degradation. The bark has an elevated ash content (17%), primarily composed of calcium, and a noteworthy extractive content (38.9%), predominantly of hydrophilic compounds. The antioxidant activity of the bark extracts is moderate, with an IC50 value of 40 μg/mL and an EC50 value of 230 μg/mL by DPPH and TBARS methods. The lipophilic extractives principally contain fatty acids and diterpenoids. The suberin content is low (1%) and composed primarily of ω-hydroxy acids with 9,10,18 trihydroxyoctadecanoic acid as the major suberin monomer. The lignin content is low (9.8%), and polysaccharides represent 33%. The ignition temperature of the bark is 190 °C, the burnout temperature is 653 °C, and the activation energy in combustion is 29 kJ mol−1. A biorefinery concept was developed considering the bark’s chemical and thermal characteristics to convert approximately 90% of the bark mass into valuable chemicals, extracts, functional materials, and additives.